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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Classification of continuous $ JBW\sp *$-triples


Authors: G. Horn and E. Neher
Journal: Trans. Amer. Math. Soc. 306 (1988), 553-578
MSC: Primary 46L70; Secondary 17C65, 46H70
MathSciNet review: 933306
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Abstract: We show that every $ JB{W^{\ast}}$-triple without a direct summand of type I is isometrically isomorphic to an $ {l^\infty }$-sum $ \mathcal{R}{ \otimes ^\infty }H(A,\,\alpha )$ where $ \mathcal{R}$ is a $ {w^{\ast}}$-closed right ideal in a $ {W^{\ast}}$-algebra $ B$ and $ H(A,\,\alpha )$ are the elements of a $ {W^{\ast}}$-algebra $ A$ which are symmetric under a C-linear involution $ \alpha $ of $ A$. Both $ A$ and $ B$ do not have a direct ( $ {W^{\ast}}$-algebra) summand of type I. In order to refine the decomposition $ \mathcal{R}{ \otimes ^\infty }H(A,\,\alpha )$ we define and characterize types of $ JB{W^{\ast}}$-triples.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933306-7
PII: S 0002-9947(1988)0933306-7
Article copyright: © Copyright 1988 American Mathematical Society